A "verge"?
According to Wikipedia, "verge" is one term (among many) for the strip of grass between the sidewalk and thre street. I'd never heard it used that way either.
verge1
[vurj]
Synonyms
Examples
Word Origin
noun
1.
the edge, rim, or margin of something:
the verge of a desert; to operate on the verge of fraud.
2.
the limit or point beyond which something begins or occurs; brink:
on the verge of a nervous breakdown.
3.
a limiting belt, strip, or border of something.
4.
British. a narrow strip of turf bordering on a pathway, sidewalk, roadway, etc.
5.
a decorative border, as on or around an object, structural part, etc.
6.
limited room or scope for something:
an action within the verge of one’s abilities.
7.
an area or district subject to a particular jurisdiction.